Photos have been shared on Twitter showing the building up in flames.
Six fire trucks and two ladder trucks were sent to the scene and there were reports that the body of a dead woman was seen on the seventh floor.
Firefighters were still unable to reach her due to the fire, the Bangkok Post said.
Meanwhile, Police fear more people may be trapped in the building's sixth to eighth floors.
Police and rescue workers are trying to reach them.
The Bangkok Post are reporting that the burning building is the home of family and relatives of Vikrom Aisiri, a former Democrat MP and owner of Phuket Air - an airline based in Bangkok.